Understanding Of Geometric Concepts Research Articles

Development of Student Worksheets Based on Calligraphy Art on the Subject of Circles

Purpose of the study: The purpose of this research is to develop a student worksheet based on the art of calligraphy on the subject of class VIII circles at State Islamic Junior High School 1 Pringsewu. This research also aims to test the validity, practicality and effectiveness of the student worksheet developed. Methodology: This research uses research and development methods (Research & Development). The research subjects were 29 class VIII students at State Islamic Junior High School 1 Pringsewu. Data will be analyzed using validation instrument data analysis techniques, student response questionnaires, and learning outcomes tests. Main Findings: The main finding of this research is the development of calligraphy-based student worksheets on the subject of class VIII circles. This student worksheets includes components such as cover, table of contents, subtitles, competency standards, basic competencies, material, discussion, conclusions and practice questions. This student worksheets has gone through a process of validation and testing in learning. Novelty/Originality of this study: Research regarding the development of student worksheets based on calligraphy art on circles revealed that the integration of art and mathematics can increase students' creativity and understanding of geometric concepts. The results of this research show that an interdisciplinary approach not only makes learning more interesting, but is also effective in strengthening students' analytical and aesthetic abilities.

Technology and geometry: Fostering young children's geometrical concepts through a research-based robotic coding program

AbstractGeometric concepts are fundamental to early geometry education, and developmentally appropriate practices are crucial for teaching them to young children. Robotic coding is an effective tool in many areas of early mathematics and has significant potential in teaching geometric concepts. This study aimed to test the impact of a research-based robotic coding program on young children's understanding of geometric concepts. A quasi-experimental design was used with two intervention groups. The study involved 52 5-year-old children from a public kindergarten. The intervention-1 group (n = 18) received a research-based robotic coding program, while the intervention-2 group (n = 16) received a research-based no-coding program. The non-intervention group (n = 18) attended their regular program. Data on participants' understanding of geometrical concepts was collected through individual interviews using a geometric shapes classification test. Hierarchical linear modeling (HLM) was utilized to assess the effectiveness of two interventions. The results showed that both interventions had a significant effect with the robotic program being more effective. Additionally, follow-up tests indicated that both interventions had a lasting effect on the children's understanding of geometrical concepts. The study highlighted the potential of incorporating robotic coding and relevant research in fostering young children's geometrical development.

ANALISIS KESULITAN PENYELESAIAN SOAL GEOMETRI PADA SD ISLAM AL AZHAR 34 MAKASSAR


 Geometry at the elementary school level brings various benefits to students. Firstly, it is a critical stage in the development of spatial abilities. Geometry helps students understand the world around them in different ways. This study aims to analyze the difficulties in solving geometry problems among elementary school students. The research design used is quantitative research with data collection techniques using tests and documentation. The research subjects are fifth-grade students of SD Islam Al Azhar 34 Makassar, consisting of 30 individuals. The research sample consists of 5 students. The results of the study indicate that visual-spatial understanding, perception, interpretation, and mathematical communication skills play a crucial role in students' understanding of geometric concepts. Student A needs to be introduced to the concept of classifying plane figures to improve their spatial understanding, while student B needs a deeper understanding of the types of plane figures. Student C needs to develop mathematical communication skills and pay attention to the instructions of the problems in order to accurately transfer their understanding of concepts. Student D has adequate conceptual understanding but needs to improve their accuracy in solving the final steps. Student E has good conceptual understanding of solving geometry problems but needs to be reminded of the importance of completing all solution steps accurately. An approach that includes introducing the concept of classifying plane figures, deepening understanding of the types of plane figures, developing mathematical communication skills, and paying attention to problem instructions needs to be implemented to enhance students' understanding of geometric concepts and their ability to solve problems accurately.

Integrating Art and Dynamic Geometry Software into the Teaching and Learning of Middle School Geometry

Abstract This study focuses on understanding the ways in which integration of art and dynamic geometry software (DGS) into geometry influenced middle school teachers’ understanding of geometric concepts that are difficult to teach, and their perceptions of teaching these topics. The study indicated that art materials combined with DGS played different roles in teachers’ understanding of geometry: in some cases, they helped acquisition of new knowledge and development of deeper conceptual knowledge while addressing misconceptions; in other cases, they helped the retention of knowledge by association with the activity; and in some cases, they facilitated the transfer of knowledge and development of strategic knowledge. Study results also indicated that integration of art combined with DGS led to a higher level of creative engagement that supported productive struggle and helped teachers appreciate and understand pedagogy differently. Lastly, the teachers made connections from learning mathematics content to the pedagogy of teaching that same content.

ETHNOMATHEMATICS VALUES IN SUMEDANG TOFU AND BONGSANG (TOFU BASKET) FOR TEACHING GEOMETRY IN PRIMARY SCHOOL

Ethnomathematics can be an option for teaching a more contextual mathematics which contributes to a successful mathematics learning. The present study highlighted ethnomathematics concepts that could be found in Sumedang’s local food, namely Sumedang Tofu, and the bamboo basket used as its container (bongsang). Mathematical concepts in Sumedang Tofu and its bongsang are related to geometry. Geometry allows students to develop their abilities in presenting or describing the order in the world or their immediate environment. Geometry learning affects students’ ability to connect mathematical ideas, both in the discipline and to other disciplines as well as the real world. The results of this study show that Primary School students still had difficulties in learning and understanding geometry. Therefore, it was necessary to develop a method that would improve students’ understanding of geometrical concepts, which were important because they were highly relevant to students’ daily life. The present study aimed to explore geometrical concepts found in Sumedang tofu and bongsang. Descriptive qualitative approach was implemented, in which the data was gathered through observation, literature study, and interviews. The findings indicated that geometrical concepts could be found in Sumedang tofu and bongsang. Those concepts could be used in mathematics lessons in primary school to provide meaningful learning for students. The results of this study could be used as a foundation to develop an ethnomathematics learning in primary school level.

Geometric Thinking Skills of Seventh Grade Students on the Topic of Triangle and Quadrilateral Based on Van Hiele Geometry Learning Theory

Students’ geometric thinking skills can describe students’ understanding of geometrical concepts. According to van Hiele, students’ geometric thinking skills is divided into five levels, namely Level 0 Visualization, Level 1 Analysis, Level 2 Informal Deductive, Level 3 Deduction, and Level 4 Rigor. The level of students’ geometric thinking skills be an indicator of the success of learning geometry. The teacher should be able to analyse the students’ geometric skills to help students to improve their geometric thinking skills. The purpose of this study was to describe the geometric thinking skills of 7th grade students of Junior High School in Boyolali, Indonesia. This type of research was quantitative descriptive research. The study was conducted by giving ten questions that correspond to the level of students’ geometric thinking skills. The results showed that as many as 26.09% of students were at level 0, as many as 56.62% of students were at level 1, as many as 17.39% of students were at level 2, and no students were able to reach level 3.

PENINGKATAN PEMAHAMAN KONSEP GEOMETRI MELALUI TAHAPAN BERFIKIR VAN HIELE DI SMP NEGERI 8 LANGSA

Understanding the concept is a benchmark students can proceed to the next stage in the learning process and the stage of thinking Van Hiele is a good solution to direct students to the actual concept of geometry. Stages of thinking Van Hiele specializes in teaching geometry. There are three main elements in teaching geometry, namely time, teaching material, and the teaching methods applied. If the three elements are arranged in an integrated manner, they will be able to improve students' thinking abilities to the higher stages of thinking. The purpose of this study was to determine whether there was an increase in understanding of the geometrical concepts of eighth grade students of SMP Negeri 8 Langsa through the Van Hiele thinking stage. This research was classified into quasi-experimental research. This study uses a One Group Pretest-Posttest Desaign research design. The population in this study were all eighth grade students of SMP Negeri 8 Langsa. Samples were taken using simple random sampling technique and students of class VIII I were selected as sample classes. The instrument of this study is the ability to understand concept tests. This test was arranged in the form of a description consisting of 6 questions. From the results of the calculation of the percentage understanding of students' geometrical concepts showed an increase of 48%. The results of data analysis obtained that count> t table is 12.59> 2.08, this means that Ho is rejected and Ha is accepted, so it can be concluded that there is an increase in understanding of students' geometry concepts through the stages of van hiele thinking at SMP Negeri 8 Langsa.
 
 Keywords: Stages of thinking Van Hiele, Ability to understand concepts and Geometry.

Play enhances visual form perception in infancy-an active training study.

Motor experiences and active exploration during early childhood may affect individual differences in a wide range of perceptual and cognitive abilities. In the current study, we suggest that active exploration of objects facilitates the ability to process object forms and magnitudes, which in turn impacts the development of numerosity perception. We tested our hypothesis by conducting a preregistered active exploration intervention with 59 8‐month‐old infants. The minimal intervention consisted of actively playing with and exploring blocks once a day for 8 weeks. In order to control for possible training effects on attention, we used book reading as a control condition. Pre‐ and post‐test assessments using eye‐tracking showed that block play improved visual form perception, where infants became better at detecting a deviant shape. Furthermore, using three control tasks, we showed that the intervention specifically improved infants' ability to process visual forms and the effect could not be explained by a domain general improvement in attention or visual perception. We found that the intervention did not improve numerosity perception and suggest that because of the sequential nature of our hypothesis, a longer time frame might be needed to see improvements in this ability. Our findings indicate that if infants are given more opportunities for play and exploration, it will have positive effects on their visual form perception, which in turn could help their understanding of geometrical concepts.

Pengaruh Pembelajaran Kooperatif Tipe STAD dengan Bantuan Website terhadap Kemampuan Pemahaman Konsep Geometri Siswa Kelas VIII

This study aims to determine the differences in STAD type cooperative learning on geometry material integrated with the website www.fooplot.com. The subject of this study was a private junior high school in Bekasi, which is consisted of 31 male students and 40 female students. This study uses a quasi-experimental design method. Data from the research will be analyzed using descriptive statistics. The results of the study have shown that learning mathematics using a website has assisted students to improve their understanding of geometric concepts. The learning with the website has supported students to study independently outside of school hours. Website applications can encourage students to examine student work independently.

An Investigation of the Effects of Measuring Authentic Contexts on Geometry Learning Achievement

Geometry students have few opportunities to apply geometric concepts and solve geometry problems in authentic contexts. We developed a Ubiquitous Geometry (UG) system to teach geometry to elementary students by using it to measure common objects in authentic contexts. The instant study investigates the effects of UG on student geometry estimation ability, geometry learning achievement, spatial ability, and learning geometric concepts and explores the correlations. Participants were 82 fifth grade students divided into the experiment group (EG), the ruler measurement group (RG), and the control group (CG). The results revealed that the EG students performed significantly better than the others in geometry estimation ability, geometry learning achievement, spatial ability, and understanding geometric concepts. We found that geometry estimation ability is significantly related to spatial ability and geometry learning achievement, which means fostering estimation ability through measuring authentic objects could help students to learn geometry. Finally, students perceived that UG engaged them more in geometry and improved their interest in learning because the activity designs related more to their daily life, thereby enhancing their sense of confidence and satisfaction. Conclusions include that UG effectively enhances student geometry estimation ability, geometry learning achievement, spatial ability, and understanding of geometric concepts.

Learners’ Interpretation Of Geometric Concepts In The Intermediate Phase: The Case Of Limpopo Province

This paper reports on an exploratory study in which questionnaires assessing the understanding of grade 4 mathematics concepts learnt as prescribed by Continuous Assessment Policy Statement (CAPS) were administered to 219 grade 5 learners from 20 randomly selected primary schools in the Limpopo province of South Africa at the beginning of the year 2014. This paper reports only on the understanding displayed in responses to five out of twelve questions that sought interpretation of geometric concepts in the questionnaires. This was a both quantitative and qualitative study in which structured and semi-structured interviews were conducted with six learners on the basis of their responses to gain more insight into how they constructed their geometric meanings. Results indicated that some learners did not understand the questions but would respond to questions based on a word or diagram that they associated with a particular concept. Nonetheless, 99% learners displayed understanding and familiarity with the concept of similarity. It can be recommended in this study that the interpretation in some questions be explained using African languages that were used in the learners’ previous grades. Also the use models like photos, diagrams, graphs, symbols, icons, and other visual representations can help promote the conceptual understanding of geometric concepts to learners in the intermediate phase. The study therefore concludes that for learners to interpret geometric concepts in the intermediate phase, their geometric vocabulary should be developed such that they are able to make connections between new ideas and their prior learning.

Students’ Concepts of the Trapezoid at the End of Lower Secondary Level Education

Abstract Understanding basic geometric concepts is important for the development of students’ thinking and geometric imagination, both of which facilitate their progress in mathematics. Factors that may affect students’ understanding include the teacher of mathematics (in particular his/her teaching style) and the textbooks used in mathematics lessons. In our research, we focused on the conceptual understanding of trapezoids among Czech students at the end of the 2nd level of education (ISCED 2). As part of the framework for testing the understanding of geometrical concepts, we assigned a task in which students had to choose trapezoids from six figures (four trapezoids and two other quadrilaterals). In total, 437 students from the 9th grade of lower secondary schools and corresponding years of grammar schools participated in the test. The gathered data were subjected to a qualitative analysis. We found that less than half of the students commanded an adequate conceptual understanding of trapezoids. It turned out that some students did not recognise the non-model of a trapezoid, or vice versa, considering a trapezoid in an untypical position to be a non-model. Our research was supplemented by analysis of geometry textbooks usually used in the Czech Republic which revealed that the trapezoid is predominantly presented in a prototypical position. Moreover, we investigated how pre-service teachers define a trapezoid. Finally, we present some recommendations for mathematics teaching and pre-service teacher training that could help.

Единый конструктивный алгоритм построения фокусов кривых второго порядка

While using conventional tools for solving geometric problems, it is difficult to obtain and analyze results where imaginary geometric images appear. Despite the recognition of legitimacy and scientific value of imaginary solutions presenting in geometric constructions, the question on such solutions’ appropriateness and practical feasibility remains no completely clear up till now. That’s why, for most practitioners imaginary solutions are presented as something unattainable or unimportant. However, the introduction of imaginary geometric images into the practice of geometric modeling makes it possible to obtain solutions in an exhaustiveness, to develop unified algorithms for solving problems that were usually presented as either not solvable or reduced to solutions in partial settings. The use of computer technologies and the paradigm of constructive geometric modeling allow eliminate this problem’s acuteness, and direct efforts both at geometric theory’s improvement and introduction of scientific achievements in this area at the field of practical applications. Automation means for geometric experiment make it possible to find new regularities in seemingly well-known mathematical facts, to come to more general understanding of geometric concepts and images. This paper is devoted to analysis of some geometric schemes and to discussion of arising from it questions related to the theory of second-order curves creation by the methods of constructive synthesis. In the paper it has been demonstrated that the currently used definitions of second-order curves’ center and diameters contradict the principle of conics indistinguishability in projective geometry. The ways for eliminating of these contradictions have been proposed, and a unified algorithm for the second-order curves’ foci creation has been developed based on these ways.

ERROR ANALYSIS GEOMETRY QUESTIONS ON WORKING CLASS V SD / MI IN YOGYAKARTA

In 2013, the results of UAN for mathematics in primary schools / MI in DIY average value is lower than other subjects, namely Indonesian and IPA. The success of the sixth grade students work on problems UAN is inseparable from the ability of students to understand math at grade material underneath. Based on the experience of researchers, many teachers who have less correct geometry concepts. Of course this is an impact on students' understanding of geometrical concepts. So in this study will be examined whether the errors are mostly done by students in grade V on the geometry of the material, especially material area and perimeter of a flat wake. This research is qualitative descriptive field. Subjects were 43 fifth grade students who come from 4 SD / MI in the city of Yogyakarta. Data retrieval by providing written test questions, the essay form. The results showed that the most frequent errors are errors of type-1, which is a misconception. Another error is the fault of type-3, namely: writing mathematical notation and use of the unit.

Teacher trainees crossing the barrier between the concrete and the abstract - (mis)understanding of geometric concepts

In general, abstraction and correct understanding of fundamental concepts play an important role in teaching practice. A good teacher not only has to know the proper meaning of concepts, but also be able to use them correctly and recognize situations in which it is sensible to use particular terms. Pupils acquire notions of terms in their early childhood and then in primary educational level, therefore primary teachers’ correct understanding of the concepts is essential. During their university studies some teacher trainees find out that they have incorrect or insufficient notion of geometric terms. This can be remedied in several ways. Useful remedy methods can be discussions, Socratic dialogue or use of various material teaching aids. We managed to interlink these three methods in a 90-minute lesson of an optional course covered in study plan of the Teacher Training Master Programme for Primary Education at Constantine the Philosopher University in Nitra, Slovakia. The students who participated in the lesson were in their first or second year of the master degree study. The submitted contribution comprises a brief description of the lesson and a summary of findings we obtained by means of worksheets filled in by the teacher trainees.

An Assessment of the Readiness of Grade 10 Learners for Geometry in the Context of Curriculum and Assessment Policy Statement (CAPS) Expectation

In 2012 January, as part of the ongoing process of curriculum revision which began in 1994, the South African Depart of Education (DoE) introduced the Curriculum and Assessment Policy Statement (CAPS). The CAPS brought Euclidean geometry with its formal proof back into the compulsory mathematics curriculum. It also implied that all learners needed to perform at level 4 (Deduction: with formal proof) of the van Hiele levels in Euclidean geometry in all grades in the Further Education and Training (FET) phase-Grades 10-12. The main aspect of the van Hiele theory is that of children's understanding of geometric concepts can be characterised as being at certain specific levels within a hierarchy of levels from 0 to 4 with level 0 being the lowest. This paper reports on the assessment based on the van Hiele model of geometrical thinking levels of a sample of South African Grade 10 learners in Euclidean Geometry. It is a follow up of an earlier published study with 191 grade 10 learners by the same authors. Data for this study were generated from 359 Grade 10 learners in five senior secondary schools in one Education District. These schools were selected through purposive sampling. The study made use of both quantitative and qualitative research techniques for data collection. In the former, multiple choice questions and in the latter, structured interviews were made use of. The quantitative and qualitative data were anlysed using Microsoft Excel 2007 and thematic analysis, respectively. The results from the study revealed that the majority of the learners were at level 0 despite the CAPS expectation that learners are to perform at level 3 in order to be ready for level 4 thinking in Grade 10. The findings from the study assisted the authors to suggest recommendations that could be made use of by curriculum developers and implementers to improve the instructional strategies of geometry learning and teaching.

Analyzing students' interaction with a 3D geometry learning tool and their teacher

Abstract This article reports on a study of students' interaction with technology, peers, and their teacher when working with geometry. The aim of this study is to understand how the interaction and the designed artifact contribute to changes in understanding of geometrical concepts. These changes are seen as students' emerging properties accomplished in social interaction with the designed artifacts and the teacher. Using descriptive statistics from pre- and posttests, we identify that students' overall score improves. Based on the pre–post score, we analyze interactions and the products of two student dyads with different learning outcomes. We combine types of data and units of analysis. Through the descriptive statistics, we derive the variations within the school class. Through the social interaction, we can identify patterns that can give new insight into how and why students develop their understanding of geometrical concepts. The analysis of the interaction shows that the teaching strategy differs based on the students' participation and display of knowledge, and the features in the designed artifact invoked in the interaction. We use a socio-cultural perspective, which makes it possible to analyze the data at different levels and discuss how it can give a robust and valid understanding of students' learning.

A Survey of South African Grade 10 Learners’ Geometric Thinking Levels in Terms of the Van Hiele Theory

The main thesis of the van Hiele theory is that childrens' understanding of geometric concepts can be classified into a sequence of five hierarchical thinking levels, with levels 1 and 5 being the l owest and the highest.However, an additional lower level, level 0, was added in by other researchers. This paper reports on a part of a larger study which focused on the van Hiele levels of geometric thinking amongst a group of Grade 10 learners. The sample consisted of 191 Grade 10 learners from five senior secondary schools in one Education District in the Eastern Cape Province of South Africa. The respective mathematics teachers in each of these schools assisted in the selection process. The schools were selected through purposive sampling. The necessary ethical r equirements were met. Participants completed a test on van Hiele levels of geometric thought by responding to questions on basic geometric concepts including the classification and properties of triangles and quadrilaterals which constituted the basis for space and shape component of the South African Grade 10 Mathematics curriculum. The data were analyzed by manual counts and by using Microsoft Excel. The study found that the majority of learners were at level 0, which is a cause for concern. The paper recommends that educators who facilitate geometry l earning in grade 10 need to familiarize themselves with the van Hiele levels in order to achieve effectiveness in the teaching/ learning interface of geometrical concepts.

Increasing Communication in Geometry by Using a Personal Math Concept Chart

The action research team developed a “Personal Math Concept Chart”. This chart required students to describe the mathematical concepts that they were studying in the Geometry strand of Mathematics using their own images and words. In this study, students were encouraged to express their own understanding of geometric concepts in order to strengthen their own personal knowledge. The purpose of the Personal Math Concept Chart was to enhance students’ ability to express themselves using mathematical terminology. As part of having students work toward improving their mathematical expression with the Personal Math Concept Chart, the teachers on this action research team invited students to connect the concepts learned in class to everyday applications.

The nature of geometry instruction and observed learning-outcomes opportunities in Nigerian and South African high schools

The purpose of this qualitative case study involving six secondary school teachers was to obtain insight into how geometry is taught in selected Nigerian and South African high schools. It also aimed, by making use of the van Hiele model of geometry instruction, to elucidate what possible learning opportunities observed instructional methods could offer learners in the subject. The sample comprised three mathematics teachers from Nigeria and three mathematics teachers from South Africa, all of whom were selected using purposive sampling techniques. Instructional activities in six geometry classrooms were recorded on videotape. The van Hiele learning phases provided the framework for data analysis. The findings of this study indicate that observed teaching methods in geometry classrooms in the participating schools offer learners scant opportunity to learn geometry. In comparative and relative terms, however, the observed instructional methods in geometry classrooms within the South African subsample offer greater opportunities for the learners to learn geometry than observed teaching methods in geometry classrooms within the Nigerian subsample. The tentative conclusion drawn is that learners whose instructional experiences align approximately with the van Hiele phases of learning demonstrate a better understanding of geometric concepts than their counterparts whose geometry classroom instructional experiences deviate significantly from the van Hiele model. Certain images of teaching evident in the videotaped lessons are discussed and some recommendations offered.